MASTER 
NEGATIVE 

NO.  94-82231 


1 


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Author: 

Ware 


J 


William  Powell 


Title: 


Prof.  Ware's  $10,000 


prize  rule  for  the... 


Place: 


Philadelphia 

Date: 

1873 


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MASTER    NEGATIVE   * 


COLUMBIA  UNIVERSITY  LIBRARIES 
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tion of  payments  ...  To  which  is  appended  Ran- 
kin's perpetual  manual.  Philadelphia,  Claxton, 
Remsen  &  Haffelfinger,  1873. 

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THE  LIBRARIES 


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PROF.  WARE'S 


$10^000 

If>RIZE    RULE 


FOK    THE 


Umim  0f  llaatn^ttb. 


Two-thirds  of  the  time  and  labor  saved — requiring  only 
one  division  in  debit  and  credit  aecoiints. 

TO  WHICH  IS  APPENDED 

RANKIN'S  PERPETUAL  ALMANAC. 


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^PBlIii^DELeHCA: 
CLAXTON,   REMSEN   &  II.>  FFELriNGER, 
624,  626&ti28  IkJAtlkEC  STH^.iPrr   '      ' 
1873. 


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Entered,  according  to  Act  of  Congress,  in  the  year  1872,  by 

Prop.  W.  Powell  Ware,  in  the  Office  of  the  Librarian 

of  Congress,  at  Washington,  D.  C. 

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1 


INDEX. 


PAGE 


Q. 
CO 

Author's  Preface, ^ 

General  Rules  of  Equation, 7 

Dr.  and  Cr.  Accounts, ^ 

Bills  on  Unequal  Time 1^ 

Bills  on  Equal  Time, ^^ 

Monthly  Statements, ^^ 

Balance  Falling  Due  prior  to  First  Transaction,..  ..19 
Computation  of  Interest  for  360  Days  per  Annum,. 20 

**  **  365      '•         "         21 

Interest  by  Cancellation,  22 

To  Calculate  Interest  for  Days, 24 

Computing  Percentage, 25 

Multiplication 27 

Diamond  or  Cliain  Rule, 29 

Multiplication  of  Fractions, 31 

Division  of  Fractions, • 32 

Guide  in  Addition, 33 

Conversion  of  Sterling  Money, 34 

Barter ^^ 

Discount, 36 

Wood  Measure,  &c 37 

Names  of  Coins, 39 

Yalue  of  Foreign  Money, 40 

Prof.  Ware's  Challenge, 45 

Decision  of  the  Judges, 46 

Magic  Square, ...   . » 47 


PREFACE. 


The  author  of  tliis  inestimable  little  book 
has  spent  several  years  as  a  teacher  in  schools 
in  different  States.    He  has  found  it  a  very 
difficult  task  (in  all  cases)  to  make  pupils 
thoroughly  understand  and  fully  comprehend 
the  rules  in  mathematics  as  they  are  generally 
laid  down  in  the  arithmetics  of  the  past  and 
present,  and  if  understood  at  all  by  them, 
would  be  forgotten    almost    before    leaving 
school,  or  at  least  a  very  short  time  after.     He 
also   spent  several  years  as  book-keeper,  in 
which  vocation  he  experienced  the  great  need 
of  short,  simple,  and  comprehensive  rules  by 
which  time  and  labor  could  be  saved  in  all 
cases,  and  especially  in  that  most  important 
in  the  whole  routine  of  commercial  transac- 
tions—viz. :  ''  Equation  of  Payments.''     The 
idea  occurred  to  him  that  improvements  might 
be  made  in  mathematics  as   well  as  in  me- 
chanics.    He  resolved  to  try,  and  after  long 
and  ardent  study,  succeeded  in  devising  and 
bringing  to  light  a  plan  so  simple  that  the 
ordinary  mind  can   fully  comprehend   and 
understand.     After  perfecting  his  system  or 
rule,  he  sought  to  impart  the  same  to  book- 
keepers and  business  men.     He  succeeded^  in 
giving  over  2,000  private  lessons,  each  of  15  to 
25  minutes,  and  in  all  cases  gave  perfect  sat- 


mmtrnm 


6 


PROP,  ware's  system  op 


isfaction,  after  which  he  offered  a  premium  of 
$10,000  for  a  better  system  than  his  own; 
failing  to  get  any  better,  he  then  put  his  system 
in  book  form,  which  is  now  being  rapidly  sold 
at  $3  per  copy  in  commercial  circles.    He  has 
from    nearly    twenty-five    years    experience 
among  business  men   and  book-keepers,  ob- 
served the  difficulty  they  have  in  recollecting 
the  ordinary  rules,  and  if  remembered,  a  vast 
amount  of  time  and  labor  has  been  lost  by 
using  them ;  he  has  also  seen  the  many  efforts 
made  to  devise  shorter  and  simpler  methods, 
and  the  disposition  to  ignore  the  rules  as  taught 
in  the  arithmetics  of  the  day.    Believing  the 
time  and  money  spent  in  the  schools  of  the 
present  day  in  that  particular  branch  to  be  a 
useless  expenditure,  and  knowing  from  expe- 
rience that  simple  things  learned  in  school 
can  be  easily  remembered  in  after  life,  he  has, 
at  the  suggestion  of  friends,  consented  to  put 
his  system  in  a  cheap  form,  that  can  be  intro- 
duced into  all  the  public  and  other  schools 
throughout  the  whoie  country,  that  the  rising 
generation  may  save  a  great  amount  of  hard 
study,  waste  of  time,  labor,  and  money,  and 
learn  something  that  will  prepare  them  for  the 
vicissitudes  of  business,  and  can  be  remem- 
bered all  their  after  life  at  a  mere  nominal 
expense.     If  such  be  the  case,  then  his  mission 
will  have  been  fulfilled  in  which  he  has  long 
sought  to  be  a  benefactor  to  the  whole  com- 
munity. 

W.  POWELL  WAEE. 


GENERAL   RULES 


or 


EQUATION 


Start  at  the  first  of  the  month  in  which  the 
first  transaction  takes  place,  instead  of  the 
date  of  the  first  bill.  Call  the  first  month  0, 
then  number  the  following  months  in  their 
regular  order,  setting  the  number  in  the  mar- 
gin, or  elsewhere. 

Each  bill  then  shows  at  sight  the  time  for 
which  the  interest  must  be  obtained. 

Note. — Compute  interest  at  1  per  cent,  per 
month.  Any  amount  of  dollars  shows  its  own 
interest  (in  cents)  for  one  month.  Point  off 
the  right  hand  figure,  and  the  interest  is  shown 
(in  cents)  for  one-tenth  of  a  month  (or  3 
days). 


sma^ 


8 


r.> 


PliOF.  WARE  S  SYSTEM   OP 


EULE. 

Multiply  tlie  tuJiole  amount  of  dollars  by  the 
number  of  months  required.  Multiply  one- 
ienth  of  the  dollars  by  one-tMrd  the  number 
of  days  required,*  setting  the  products  under 
each  other  until  all  the  interest  is  obtained ; 
add  up  the  interest,  annex  two  ciphers  to  the 
right,  and  divide  by  the  footing  of  the  bills 
(in  dollars  only) ;  the  answer  will  be  in  months 
and  hundredths  of  months.  Multiply  the 
hundredths  by  30  to  bring  it  into  days. 

N.  B. — Add  the  month  in  the  margin  to 
those  in  the  face  of  the  bills  in  all  cases  of 
unequal  time. 

*NoTE. — One-third  of  any  number  of  days 
shows  how  many  tenths  are  contained  therein. 

EXAMPLE. 

24  days  contain  8  tenths,  25  days  8|^  tenths, 
20  days  8f  tenths,  27  days  9  tenths,  &c. 


k 


EQUATION  OF  PAYMENTS. 


9 


DEBIT  AND  OEEDIT  ACCOUNTS 

0?  ALL  CLASSES. 
{To  find  tnlwri  f.ie  balance  is  due) 

KULE. 

Arrange  the  time,  commencing  at  the  first 
of  the  month  on  which  the  first  transaction 
took  place,  whether  debit  or  credit.  Then 
compute  the  interest  on  both  sides  of  the  ac- 
count for  the  time  called  for  in  each  bill; 
subtract  the  smaller  amount  of  interest  from 
the  larger,  annex  two  ciphers  to  the  right  of 
the  difference  in  interest  (read  so  many  cents), 
and  divide  by  the  balance  of  the  account.  As 
many  months  and  days  as  are  obtained  in  the 
quotient,  or  answer,  so  long  will  the  balance 
fbe  falling  due,  from  the  cipher  or  starting 
'  point. 


10 


PROF,    ware's   system   OF 


1871 


1872 


EXAMPLE. 
Dr. 

0,  July  27,  Mds.  4  mos 1350  I   ?!?? 

4,  Nov.  12,    "      6    "    2531  p-JJ  {^ 

6,  Jan.  18,    '•     5    " 1940  [^JJJJ 

9  Apr.  21,  Cash 117o[l^|-|J 


16991  $667.90 


1^1 

w 
III 


Cr. 


1871 


1872 


l.Aug.    9,  Cash 750  I-  I  [^ 

3,  Oct.     5  *Dft.  90  days  961  !^  ^J  ^^H 

9,  Apr.     6,  Cash 850  ^-  "^'  ^^ 

^^"i  1.70 

\  2.50 


13,  Aug.  15,  Note  60  days 500  [    '^?  ^^ 


$3061  $221.71 


I 


Br.  Int 66.790 

Cr.   Int 22.471 


13930 


Balance ....  3930)443 1 9 .  00(1 1 .  27 

30 


8.10 
11m.  8^  from  July  Ut. 


Balance  due  June  8,  1872. 


%  K 


5  days  If  tenths,  or  ^  of  961, 


j 


1' 


^ 


EQUATION  OF  PAYMENTS. 


11 


Commence  July  0.  From  July  1st  to  No- 
vember 1st,  is  4  months ;  to  January,  6  months ; 
to  April,  9  months.  From  July  to  August,  1 
month;  to  October,  3  months;  to  April,  9 
months ;  to  August  next  year,  13  months. 

Eead  the  bills :— 1st,  you  want  the  interest 
for  4  months  and  27  days ;  2d,  10  months  and 
12  days;  3d,  11  months  and  18  days;  4th,  9 
and  21  days;  5th,  1  month  and  9  days;  6th, 
6  months  and  5  days ;  7th,  9  months  and  6 
days ;  8th,  15  months  and  15  days. 

Now  obtain  the  interest : — 

1  month,  at  1  per  cent,  per  month,  is  $13.50  ; 
4  months  is  four  times  as  much,  $54.00 ;  one- 
tenth  of  a  month  is  one-tenth  of  $13.50,  which 
is  $1.35;  27  days  being  nine-tenths,  is  nine 
times  $1.35,  which  is  $12.15;  10  months  is 
ten  times  $25.31,  which  is  $253.10;  12  days  is 
four  times  $2.53=$  10.12;  and  so  on  through 
the  whole  account. 

Add  up  the  interest  of  the  Dr.,  then  the  Cr.; 
subtract  the  smaller  from  the  larger  amount, 
bringing  down  the  difference,  omitting  the 
point  between  the  dollars  and  cents ;  place  a 
point  to  the  right  of  whole  amount,  then  add 
two  ciphers  to  the  right  of  the  point,  and  di- 


.' 


I 


vide  the  difference  of  interest  by  the  balance 
ot  the  account.    As  often  as  the  divisor  is 
contained  in  the  dividend,  up  to  the  point,  so 
many  months  you  get ;  add  one  cipher  and 
divide,  that  will  give  you  tenths  of  months : 
add  the  other   cipher  and  divide,  that  will 
give  you  hundredths  of  months.     Your  an- 
swer will  read  11  months  and  27  hundredths 
of  a  month.     Multiply  the  hundredths  bv  30 
which  will  bring  the  time  into  days,  37x30 
—8  days  and  ten  one-huudredths,  which  is 
never  counted  unless  fifty  one-hundredths  or 
upward.     Thus  the  answer  is  11  months  and 
8  days  from  July  1  (inclusive),  1871,  balance 
due  June  8,  1873. 

N.  B.— Now  comes  in  the  regular  rate  per 
cent.  Any  number  of  days  that  the  balance 
IS  paid  hefore  the  8th  of  June,  the  interest  is 
taken  off  at  the  legal  rate.  Any  number  of 
days  after  the  8th  of  June  the  interest  is  added 
at  the  legal  rate. 


1873. 


1872. 


EQUATION  OV  PAYMENTS. 


18 


EXAMPLE. 
Dr. 


10.92 


0,Jau.    9,Mds.6mos 181.7.j*|    "^g^ 


0.    "     21, 
3,  Mar.    1, 

2,  "     24, 

3,  Apr.  22, 


i.i        <(        ( 


~*^"-"^    /    1.75 
"    "     ** 380.50   ]  ^^-^3 

150.10    ^    ^^^ 

L 27.00 

800.00   \    2.10 
.10 


U        ((        u 


«       <<       ii 


Cr. 


$1262  60  $101.22 


1,  Feb.    6,  Cash ^^^  |  "^ . 

2,  Mar.  16,  30 clays 200 1  ^; 


2, 


<< 


27,60 


(< 


50 

30 

6.00 

07 

"^"^  I  1.80 


$550  $18.67 


Dk.  Int 10122 

Cr.  Int 18.67 


Bal.    $712  60 


713)8255:00(11.57 

30 


17.10 
11m.  lid  from  Jan,  1st. 


Balance  due  Dec.  17,  1872. 


*  Bills  containing  Dollars  and  Cents,  the  cents  are  omirted 
if  under  fifty;  and  counted  as  one  dollar  if  fifty  or  upward. 


rT"^^"^'^™^^^" 


BILLS  BOUGHT  ON  UNEQUAL  TIME, 

{without  credit.) 

EULE. 

Compute  the  interest  on  each  bill  for  the 
time  called  for  in  the  several  bills ;  add  up  the 
interest ;  annex  two  ciphers  to  the  right  of  the 
whole  amount,  and  divide  by  the  footing  of 
the  bills,  (the  dollars  only).  The  number  of 
months  and  days  obtained  in  the  quotient, 
will  show  how  long  the  amount  will  be  in 
falling  due  from  the  0,  or  starting  point. 

EXAMPLE. 

Dr. 

1871.  0,  May    6,  Mds.  3  mos $931  j  27.93 

\    1.86 
0,    "      13, 

2,  July    9, 
4,  Sept.    1, 

1872.  8,  Jan.  27, 


(( 


(( 


i( 


4 
5 


a  o/>/v  I  17.20 

^^^\    3.44 

(      .29 

"     432J25.92 

/    1.29 

**     384  j  34.56 


2928)14118.00(4.82 
11712  30 


i      .13 
Cash 321  (25.68 

(    2.88 
$2928    141.18 


24060     24.60 
23424 


6360    4  mos.  25  d.from  May  1. 
Due  Sept.  25,  1871. 


EQUATION  OF  PAYMENTS. 


15 


Commence  May  0— July,  2  months;  Sep- 
tember, 4  months ;  January,  8  months. 

Eead  the  bills— 1st  bill,  3  months,  6  days; 
2d  bill,  2  months,  13  days ;  3d  bill,  2  and  4  are 
6  months,  9  days;  4th  bill,  4  and  5  are  9 
months,  1  day;  5th  bill,  8  months,  27  days. 

Compute  the  interest — 3  months  is  3  times 
$9.31=$27.93;  6  days  is  twice  93c.=$1.86 ;  2 
months  is  twice  $8.60=117.20;  13  days  is  4^ 
times  86c.,  &c.,  &c. 

N.  B. — Multiply  the  whole  amount  of  dollars 
by  the  number  of  months;  one-tenth  the 
dollars  by  one-third  the  days. 


\\ 


BILLS  BOUGHT  ON  EQUAL  TIME. 


EULE. 

Compute  the  interest  for  tlie  time  that  each 
bill  calls  for,  up  to  the  date  of  purchase.  Add 
up  the  interest,  annex  two  ciphers,  and  divide 
by  the  footing  of  the  bills  (the  dollars  only). 

The  months  and  days  obtained  in  the  quo- 
tient will  show  the  average  date  of  purchase, 
from  the  0. 

Add  the  time  of  credit  (whatever  it  may  be) 
to  the  average  date,  and  that  will  show  the 
date  of  maturity. 

N.B. — The  answer  always  comes  in  months 
and  hundredths  of  months.  Multiply  the 
hundredths  by  30,  which  will  give  the  number 
of  days. 


" 


B^adhiriftaMb*dfiM*H 


=n 


EQUATION  OF   PAYMENTS. 


17 


EXAMPLE. 

Dr. 
1871.     0  Feb.     0,     Omos $430  j    1-^^ 

2  Apr.  13,  "  "  384J    ^-^ 

5  July    G,  ^'  ''  ^'^^j^^'46 

5  July  21,  -  -  ^^M^2:66 

7  Sept.    2,  **  ''  431  i  30.17 

$1856    74.74 

1856)7474.00(4.02 

30 

.60    4m.  Id,  from  Feb,  Ist. 
Average  date,  June  1st — due  6  mos. 

Head— 1st  bill,  9  days;  2d  bill,  2  months, 
13  days  ;  3d  bill,  5  months,  6  days ;  4th  bill,  5 
months,  21  days;  5th  bill,  7  months,  2  days. 

4 

Compute  the  interest — 9  days  is  3  times 
43c.;  2  months  is  twice  $3.84 ;  13  days  is  4^ 
times  38c.;  5  months  is  5  times  $2.30 ;  6  days 
is  twice  23 ;  5  months  is  5  times  $3.81 ;  21 
days  is  7  times  38c.;  7  months  is  7  times  $4.31 ; 
2  days  is  f  of  43. 


_22^ 


18  PROF,  ware's  system  of 

MONTHLY   STATEMENTS. 

KULE.     ' 

Compute  the  interest  on  each  bill  for  the 
number  of  days  tliat  each  bill  calls  for. 

Acid  up  the  interest,  annex  two  ciphers,  and 
divide  by  the  footing  of  the  bills. 

N.  B. — In  a  monthly  statement  the  answer 
will  always  be  in  hundredths  of  months. 

EXAMPLE. 

1871.     Jan.    9, I87j    .54 

"    10, ^^^y'it 

"      11, 231^    -^^ 

/     .15 

"      13,...   438ll.75 

"      18, ..  217J1.30 

"      32, ^llj^S 

"     34, 221^  1176 

''     37, 407^  3.66 

"     30, 386^3.86 

*'     31, 999J^J^ 

4078  28.57 
4078)2857. 00(.  70 

30 

21.00    21  daps. 
Due  January  21. 

Compute  the  interest  for  9  days,  10  days, 
11  days,  &c.  9  days  is  3  times  18c. ;  10  days 
is  3^  times  68c. ;  1 1  days  is  3f  times  23c. ;  12 
days  is  4  times  43c.,  &c. 


EQUATION   OF  TAYMENTS.  19 

Balance  Falling  Due  Prior  to  the  Pirst  Transaction. 

EXAMPLE. 

N.  B.— Work  as  before. 

Dr. 

{    3  75 
1870.     0,  July    4,     Mds $3750  ]    ^;25 

0     ''     21         "     2000^  14.00 

O',    *'     27^       "     1850^  11).  65 

2!sept3;       -     1220J^J:g 

3,Oct.i6,     "    90o|^J;J5 

.30 

$9720    93.07 
Cr. 

1870.       4,  Nov.  24,  Cash, |500  j    ^J;  JJ 

5,  Dec.    1,  Dft.  30  days, 850  j    ^^'^ 

IS71.       8,Mar.    6,  Cash, ^^j      1.20 

(  104-  00 
10,  May    1,  Note  90  days, 800 1  ^"*;27 

$2750    238.75 

Bal $6970 

238 .  75 — greater  interest. 
93 .  07 — smaller  interest. 

1970)13568.00(1.94 
6970  30 

65980     28.20—1  m.  28d,  back  of  July  1. 
62730 

32500  Balance  due  May  2d,  1870. 


-4 


If  Ihe  interest  of  the  smaller  side  of  the  ac- 
count exceeds  that  of  the  larger  side,  the  time 
counts  loch  from  the  starting  point.  In  the 
above  example,  the  smaller  exceeds  the  greater 
by  $130.68,  throwing  the  balance,  1  month 
and  28  days,  back  of  July  1st. 

-N".  B.— The  interest  must  be  paid  from  May 
2d  up  to  the  day  of  settlement,  at  the  legal 


COMPUTATION  OF  INTEREST. 

(For  360  days  per  annum,) 

EULE. 

First  obtain  the  interest  at  12  per  cent,  per 
annum  for  the  required  time ;  then  divide  the 
product  by  13,  which  will  give  the  interest  at 
1  per  cent,  per  annum.  Multiply  this  quo- 
tient by  the  rate  per  cent,  required.  The  re- 
sult will  be  the  answer  in  cents. 

EXAMPLE. 

What  is  the  interest  on  $1850  for  7  months 
and  27  days,  at  9  per  cent,  per  annum. 


EQUATION  OP   PAYMENTS. 


21 


SOLUT10l!f. 


$1850  7  mos.,  37  days,  at  9  per  cent. 

12950 
1665 


12)146.15 

12.18 
9 


$109.62— ^7W. 

One  month  is  $18.50  ;  7  months  is  7  times 
as  much;  one-tenth  is  $1.85;  27  days  (being 
nine-tenths)  is  nine  times  as  much. 

Add  up  and  divide  the  product  by  12,  which 
is  $12.18,  at  1  per  cent,  per  annum;  9  per 
cent,  is  9  times  $12.18;  8  per  cent,  would  be 
8  times  $12.18 ;   5  per  cent.,  5  times,  &c.,  &c. 


COMPUTATION  OF  INTEREST. 

(For  365  days  per  annum.) 

RULE. 

Multiply  the  principal  by  the  number  of 
days ;  then  add  one  one-tenth  of  the  product 
to  itself;  then  add  one-half  of  the  one-tenth; 
add  up  the  whole  amount.  If  7  per  cent,  is 
required,  divide  the  product  by  6.  If  6  per 
cent,  is  required,  divide  by  7. 

J^^  Point  one  for  mills. 


22 


PROF,  ware's   system  OF 


EXAMPLE. 

What  is  the  interest  on  $875  for  120  days, 
at  7  per  cent,  per  annum  (of  365  days)  ? 

SOLUTIOI^. 

$875  120  days  at  7  per  cent. 


105000 

10500—1  tenth. 
5250— i  of  1  tenth. 


6)120750 


$20. 12.5—^72^. 


' 


FOR  COMPUTING  INTEREST 


BY  CANCELLATION. 


EXAMPLE. 


What  is  the  interest  on  $180  for  3  years,  7 
months,  and  18  days,  at  8  per  cent,  per  annum. 


i 


4 


SOLtJTIOX. 

i$0  Principal,  60 
316  time. 

120 
$  per  cent.  2 

Ans.—%37.92.0 


'• 


EQUATION   OF   PAYMENTS. 


23 


1st. — Draw  a  perpendicular  line,  place  the 
principal  on  the  right,  bring  the  years  and 
months,  to  months,  take  i  of  the  days  and 
place  to  the  right  of  the  months,  setting  the 
time  under  the  principal,  and  the  rate  per 
cent,  (whatever  it  may  be)  under  the  time ;  on 
the  left  (in  all  cases)  place  3  and  4.* 

2d. — Divide  with  the  numbers  on  the  left, 
through  any  number  on  the  right  which  they 
will  divide  without  a  remainder,  cancelling 
each  number  as  you  use  them ;  then  multiply 
all  the  uncanceled  numbers  together  on  the 
right,  and  divide  (if  any)  by  those  on  the  left. 
The  answer  will  come  i:i  mills,  if  days  be  in 
the  time;  if  no  days,  in  cents. 

3d. — If  there  be  one  over  in  taking  the  jV  of 
the  days,  place  a  3  to  the  right  of  a  decimal 
point;  thus  2  years,  7  months,  19  days,  equal 
31G.3 ;  if  two,  place  a  G ;  thus  1  year,  5  months, 
20  days,  equal  176.G— working  as  a  whole 
number  until  done.  Cut  off  in  your  answer 
o:ie  figure  for  each  figure  to  the  right  of  a 
decimal  point  or  points. 

4th.— For  days  only,  place  the  principal,  whole  number  of 
days,  and  the  rate  per  cent,  on  the  right,  placing  3,  3  and  4  on 
the  tleft,  working  by  rule  2d;  the  answer  will  be  in  mills. 


♦  The  3  and  4  stand  for  the  12  months  In  the  year. 
t  The  3, 3  and  4  stand  for  360  days  in  the  year. 


^ 


24 


PROF,  ware's  system   OP 


EXAMPLE  FOE  DAYS. 

What  is  the  interest  on  $720  for  36  days  at 
9  per  cent,  per  annum. 


3 


720 
3$ 

9 


Ans.—%^A^S) 


If  the  numbers  will  not  divide,  multiply  all 
the  right  hand  side  together,  and  divide  by  the 
left  multiplied  together,  the  quotient  will  be 
the  answer. 

If  fractional  rates  per  cent,  occur,  bring  it 
to  an  improper  fraction,  placing  the  numerator 
on  the  right,  the  denominator  on  the  left, 
working  as  before. 


SHOET  METHOD  TO  OALOULATE  INTEEEST. 

EULE. 

Multiply  the  principal  by  half  the  number 
of  days ;  that  product  divided  by  30  will  give 
the  answer  in  cents. 


EQUATION   OF  PAYMENTS. 


25 


EXAMPLE. 

What  is  the  interest  on  $165  for  16  days  at 
6  per  cent.  ? 

165  dollars. 

8  half  the  number  of  days. 
3.0)132.0 


.  44  cents. 
Divisors  for  Different  Bates  Per  Gent. 

Any  amount  multiplied  by  the  time  in  days, 

as  per  example :  $200  for  19  days,  and  divide 

by  72,  will  give  you  the  interest  at  5  per  cent. 

per  annum. 

Ans.  $.52.7. 

At  6  per  cent,  as  above,  divide  by  60 


''     7  per  cent, 

♦  • 

u 

52 

*•    8  per  cent, 

u 

45 

*•    9  per  cent, 

i< 

40 

*'  10  per  cent. 

i( 

ae 

**  12  per  cent, 

4( 

ao 

"  15  per  cent, 

« 

24 

"  20  per  cent. 

(( 

18 

*'  24  per  cent. 

ii 

15 

*'  40  per  cent, 

t( 

09 

COMPUTING-  PERCENTAGE. 

To  ascertain  what  is  gained  or  lost  by  selling 
ail  ARTICLE  for  which  a  specified  sum  has  been 
paid. 


EuLE. — Annex  two  ciphers  to  the  selling 
PRICE,  divide  by  the  cost.  The  difference 
between  the  quotient  and  100  will  be  the 
gain  or  loss  per  cent. 

Example. — Paid  5  dollars  for  a  book,  and 
sold  it  for  8  dollars.    AVhat  per  cent,  did  I  gain  ? 

Operation —  5)800 

1 .  GO    Ans. — 60  per  cent. 

Example.— Paid,  10  dollars  for  a  hat,  and 
sold  it  for  8  dollars.    What  per  cent,  did  I  lose  ? 

Operation—  10)800 

80 
Ans. — 100  less  80=20  per  cent. 

To  ascertain  what  an  article  should  be  sold 
for,  which  cost  a  specified  sum,  so  as  to  gain 
a  proposed  per  cent. 

EuLE.— Multiply  the  cost  by  100,  with  the 
per  cent,  added ;  cut  off  two  figures  to  the 
right.  The  figures  at  the  left  will  show  the 
PEICE  for  which  the  article  must  be  sold. 

Example. — Paid  30  cents  per  yard  for 
CLOTH ;  for  how  much  must  I  sell  it  so  as  to 
realize  20  per  cent,  profit  ? 

Operation —  dO^cost. 

120 — 100  per  cent  added. 


36.00    I  must  sell  it  for  36  cents. 


, 


' 


EQUATION  OF  PAYMENTS. 


27 


MULTIPLICATION. 


EXAMPLES. 


In  multiplying,  it  is  easier  to  multiply  by 
2,  3,  4,  and  5,  than  by  7,  8,  or  9,  &c. 

I  shall  now  present  examples  in  Multipli- 
cation. 

1.  Multiply  428  by  15. 

428X15  ^   place   the  15  at   the 

2140  right  of  428,  and  use  the  sign 

of  Multiplication  ;    but  this 

6420  is   iiot   necessary,  from   the 

fact  that  it  may  be  placed  anywhere  or  not 
written  at  all ;  this  of  course  is  left  to  the 
choice  of  the  operator. 

I  first  multiply  by  5,  placing  the  first 
product  figure  one  place  to  the  right;  5  times 
8  is  40 ;  then  5  times  2  equal  10,  and  the  4 
that  I  carried=14,  write  the  4  under  the  8 ; 
thus  proceed ;  then  add  the  two  products  for 
the  answer. 


38 


PROF,  ware's  system  OP 


2.  Multiply  8844  by  14. 

8844X14 
35376 


123816 


3.  Multiply  64827  by  36. 

64827X36     ^^ 
§  Commence  with   3,  then 

194481         multiply  that  product  by  2, 

388962       placing  the  first  product  figure 

^^~rr"      in  the  place  of  units. 

4.  Multiply  87234  by  39. 

87234X39 


261702 
785106 

3402126 


I 


)■ 


EQUATION  OF   PAYMENTS. 


29 


THE  DIAMOND  OE  CHAIN  EULE. 


1st.  Draw  a  perpendicular  line. 

2rf.  Arrange  the  numbers  on  opposite  sides 
of  the  line,  a^irected. 

M.  Then  cancel  on  opposite  sides  of  this 
line  all  equal  figures  and  numbers. 

Uh,  If  there  are  ciphers  on  both  sides  of  the 
line,  cancel  the  same  number  on  each  side. 

bth.  If  any  number  on  one  side  will  divide 
any  number  on  the  opposite  side,  cancel  both 
numbers,  placing  the  quotient  on  the  side  of 
the  larger  number. 

Qtli,  If  any  two  or  more  numbers  multiplied 
together  equal  one  or  more  numbers  on  the 
opposite  side,  cancel  all  those  numbers. 

"Hth.  If  any  number  greater  than  unity  will 
divide  two  numbers,  one  on  each  side,  without 
a  remainder,  cancel  both  numbers,  placing  the 
quotients  on  the  right  and  left  of  the  numbers 
divided. 


Sth.  Then  multiply  the  figures  that  remain 
on  the  right  hand  for  a  dividend,  and  those 
on  the  left  for  a  divisor. 

Wi.  Then  divide  the  product  of  those  on 
the  right  by  the  product  of  those  on  the  left ; 
the  quotient  arising  from  this  division  will  be 
the  answer. 

EEMARKS. 

Should  the  divisor  exceed  the  dividend,  the 
answer  will  be  a  fraction. 

If  the  numbers  will  not  cancel,  then  multi- 
ply those  together  that  are  on  the  right  for  a 
dividend,  and  those  on  the  left  for  a  divisor. 
Then  divide,  and  the  quotient  arising  from 
this  division,  gives  the  answer. 

This  rule  may  be  considered  as  a  pair  of 
scales  when  exactly  counterpoised;  for  we 
may  add  or  subtract,  multiply  or  divide — in 
fact,  may  do  any  thing  to  one  side,  so  long  as 
we  do  the  same  to  the  other  side ;  for  our  ob- 
ject will  be,  not  to  destroy  the  balance  or 
equilibrium. 

In  this  rule,  also,  the  same  principle  acts  as 
in  the  scales;  for  we  take  those  things,  the 
value  of  which  we  know,  to  ascertain  the 
value  of  those  which  we  do  not  know. 


:l 


\ 


N. 


EQUATION  OF  PAYMENTS. 


31 


MULTIPLTOATION  01  lEAOTIONS. 

Place  the  numerators,  both  of  the  multi- 
pliers and  multiplicand,  on  the  right,  and  the 
denominators  of  both  on  the  left  of  the  line, 
then  proceed  to  cancel  all  figures  of  equal 
value  on  the  right  and  left ;  those  uncanceled 
show  the  answer. 

Examples.— 1.  Multiply  ^^  by|  of  |  off  of 
I  of  f  of  I  of  I  and  show  the  answer. 


t 

9 

$ 


1 

t 


-Ans.  \ 


2.  Multiply 

3.  Multiply 

4.  Multiply 

5.  Multiply 

6.  Multiply 

7.  Multiply 

8.  Multiply 

9.  Multiply 

10.  Multiply 

11.  Multiply 

12.  Multiply 


ibyfoffoffofT^V 

ioff  of|-byxVofi|• 
l  of  i  of  i  by  U  of  H- 

I  of  I  by  f 

I  of  ^s  by  tV  of  tV 

lofxVofAbyiiof^off 
-^  of  f  of  I  of  I  by  i  of  T^. 
i  of  I  of  I  of -I  by  f  of  |. 

iofiofTiVoffof|byf. 
ioffbyf  ofj-Vofi 


A.    \. 
A.    i. 

A.    f 

A.  -j^. 

A.  ^. 

A.  ^. 

A.  ^V 

^■^' 
A.    f 


I 

1 


DIVISION   OF   FRACTIONS. 


Place  the  numerators  of  the  divisor  on  the 
lelt,  and  the  denominators  on  the  right,  but 
place  the  dividend  as  in  multiplication.  If 
whole  numbers  are  joined  to  a  fraction,  reduce 
as  in  multiplication. 

PEOBLEMS. 
1.  Divide  i  of  |  of  f  by  |  of  -/g-  of  f 


0 

1 

$ 

0 

7 

4 

t 

$ 

$ 

n 

0 

t 

4-  Ans. 

2.  Divide  \\>j  \. 

3.  Divide  \\>^  \. 

4.  Divide  f  by  \. 

5.  Divide  \  by  |. 

6.  Divide  \  by  |. 

7.  Divide  ^  by  |. 

8.  Divide  |  of  |  by  f  of  |. 

9.  Divide  I  <  f  I  off  l)v  |  of  ||. 

10.  Divide  1  of  I  by  1  ' 

11.  Divide  1  of  i  by  |. 

12.  Divide  i  of  ^  by  i  of  \. 


A.    \. 
A.  If 

A.  |. 
A.  If 
A.  If 
A.  f. 
A.  1. 
A.  \. 
A.    1. 


13.  Divide-|of  I  byf  of5. 

14.  Divide  \  o:  J-  by  f  of  10. 

15.  Divide  I  of  I  by  f  of  12. 
K;.  Dividj  J-of2  by  ^  of  4. 

17.  Divide  J- of  4  by  I  of  8. 

18.  Divide  liby4. 

10.  Divide  'l\  by  ^  of  5. 

•-^0.  Divide  I'ofG  by2f  of3. 


A.    f. 
A.  ^. 

A-  -5^. 
A.    1. 

A.  1. 

A.  |. 

A.  1. 

A.  \. 


SAFE    GUIDE    IN   ADDITION. 

RULPl 

111  addition  put  down  the  Avhole  amount 
until  done.  The  left  hand  figure  shows  the 
amount  to  be  carried  to  the  next  column,  the 
right  shows  the  answer. 


EXAMPLE. 

13467 

34 1st  column 

46329 

23  ...2d 

72548 

28. . .  .3cl 

9302 

25....4tli 

57831 

4 last      " 

46357 

Q                   H               it 

/^  •  •  •  • 

245834    Ans, 


N.  B. — In  the  last  addition  put  the  figure 
in  the  right  hand  column. 


I  i 


■r>Tk¥l 


34 


PROF,   ware's   system   OF 


OOKVEESION  OF  STEELING  MONET. 

EULE. 

Place  a  cipher  to  the  right  of  the  pence,  di- 
vide by  12;  add  the  shillings,  divide  by  20; 
then  add  the  i^onnds.  Multiply  the  whole  by 
40,  and  divide  the  product  by  9.  Point  off  in 
the  answer  one  figure  for  each  decimal. 

EXAMPLE. 
How  many  dollars  are  there  in  £50  7s.  6d  ? 

12)00 
2,0)7,  5 


50  375 
40 

9)2015000 

$223.88.8    par  value. 

SOLUTIOX. 

Multiply  by  40,  because  in  £1  there  are  40 
!  sixpences ;  divide  by  9,  because  $1  is  equiva- 
lent to  4s.  Gd.  at  par.     In  4s.  6d.  there  are  9 
sixpences. 


I- 


EQUATION  OF  PAYMENTS. 


35 


BARTER. 

^ 

Place  the  given  quantity  of  the  commodity 
and  the  price  at  which  it  is  valued,  on  the 
right  of  the  line.  Place  on  the  left  the  con- 
stituents of  the  commodity  whose  value  is 
required. 

EXAMPLES. 

1.  How  much  cloth  at  22  cents  per  yard, 
must  be  given  in  exchange  for  4400  lbs.  of 
cotton,  at  3^  cents  per  pound  ? 


^ 


MOO 

7 

700 


Ans.  700  yds. 


2.  How  much  tea,  at  64  cents  per  pound, 
must  be  given  for  448  pounds  of  coffee,  at  20 
cents  per  pound  ?  *      Ans.  140  lbs. 

3.  How  much  wheat  at  $1.25  cents  per 
bushel,  must  be  given  for  fifty  bushels  of  rye, 
at  70  cents  per  bushel  ?  Ans.  28  bush. 

4.  How  many  bushels  of  rye  worth  70  cents 
per  bushel,  must  I  give  for  28  bushels  of 
wheat,  the  wheat  valued  at  $1.25  per  bushel  ? 

Ans.  50  bush. 


I 


30 


piioF.  wake's  system  of 


5.  How  many  pounds  of  coffee  can  I  have  in 
exchange  for  28  lbs.  of  butter,  valued  at  21 
cents  per  lb.;  the  value  of  the  coffee  is  12  cts. 
V^Y  lb  ?  Ans.  49. 

G.  How  many  sheep  at  H  per  head,  must  I 
give  for  G  cows,  at  $12  a  piece  ?       Ans.  18. 

7.  Sold  28  bushels  of  wheat  at  75  cents  per 
bushel;  how  many  barrels  of  salt  can  I  have 
in  exchange  at  $2  per  barrel  ?        Ans.  10|. 

8.  How  much  coffee  at  20  cents  per  pound, 
must  I  give  for  120  yards  of  cloth,  at  64  cents 
per  yard  ?  Ans.  384. 

9.  How  many  bushels  of  wheat  will  pay  for 
40  barrels  of  pork  at  $8  per  barrel,  when  wheat 
is  worth  80  cts.  per  bushel  ?     Ans.  400  bush. 


DISCOUNT. 

Diacaunt  is  an  alhwance  made  far  prompt  payment 
BISCOUKT   WITHOUT  TIME. 

Place  the  sum  on  which  the  discount  is  to 
be  made,  and  the  rate  per  cent,  on  the  right, 
and  one  hundred  on  the  left. 

Example. — What  is  the  discount  on  $400, 
at  G  per  cent Ans.  $24. 


'' 


i 


I  QUATIOX   OP    PAYMENTS. 


37 


WOOD  MEASURE,  &c. 

liULE. 

Place  the  length,  height,  and  width,  on  the 
right;  on  the  left  place  the  dimensions  of  one 
cord. 

EXAMPLE. 

HoAv  many  cords  cf  Avood  in  a  pile  120  feet 
long,  12  feet  high,  and  4  feet  wide  ? 

.^10  15 

1$  3 

,4  _ 

Ans.  45  Cords. 

SOLUTIOIS'. 

4  equals  4;  4  into  12  three  times;  8  into 
120,  15  times;  3  times  15  is  45  cords. 

How  many  cords  of  wood  in  a  pile  32  feet 
long,  12  high,  and  4  Avide  ? 

n       4 

It  3 

A  — 


15 


Ans.  12  Cords. 


How  many  yards  of  carpeting  will  it  take 
to  carpet  a  hall  18  l)y  20  feet  ? 

1^  2 

0     20  — 

Ans.  40  Yards. 
Note. — Divide  by  9,  because  9  squaic  feet 
make  1  square  yard. 


38 


PROF,  ware's  system  OP 


If  i  of  6  be  3,  what  will  the  i  of  20  be  ? 

3 
3 
1 

20 

Ans.  74. 


1 
6 
4 


How  many  bricks  in  a  wall  40  feet  long,  12 
feet  high,  and  1 '  feet  thick  ?  Size  of  brick,  8 
by  4  by  2  inches. 


8 
4 
3 
2 


4C 

12 
4 


1728in.=  l  cubic  ft. 

Answer  17,280  5ricA:s. 

How  many  feet  board  measure  in  the  floor 
joists  of  a  building  18  by  40  feet,  joists  3  by  8 
inches,  placed  16  inches  apart  from  the  centre 
of  each  ? 

40 

18 

16      3 

8 

Answer  lOSO  feet. 

How  many  dollars  will  it  cost  to  carpet  a 
hall  24  by  15,  carpet  one  yard  wide,  at  11 
shillings  per  yard? 


9 

8 


24 
15 
11 


Aaswer  $55 


EQUATION   OF   PAYMENTS.  39 

BRAZIL.  D    c  M 

Johannes,  (half  in  proportion) 17  06  8 

Dobraon 32  71  4 

J^obra 17  30  5 

Moidore,  Oialf  in  proportion) 6  56 

Crusado g^  g 

ENGLAND. 

Guinea,  half  in  proportion 5  n  g 

Sovereign,  do  4  ^5 

Seven  Shilling  Piece. ...    1  70  6 

FRANCE. 

Double  Louis,  coined  bcf  1^80 9  69  3 

Louis,  coined  before  1786 4  84  4 

Double  Louis,  coined  since  178G 9  IG  3 

Louis,  coined  since  1786 4  58  1 

Double  Isapoleon,  or  forty  francs 7  71  3 

Kapoleon,  or  twenty  francs 3  86  6 

COLUMBIA. 
Doubloons 15  53  g 

MEXICO. 
Doubloons,  shares  in  proportion 15  53  8 

PORTUGAL. 

Dobraon 32  71  4 

^obra 17356 

Johannes 17  qq  8 

Moidore,  lia.lf  in  proportion 6  56 

Piece  of  16  testoons,  or  1600  rees 2  12  5 

Old  Crusado  of  400  rees 58  6 

New  Crusado  of  480  rees 63  7 

Millree,  coined  in  1755 78 


i    h 


40 


PROF,  ware's   system  OF 


SPAIN. 

D     C  M 

Quadruple  pistol,  or  Doubloon,  1772,  double 

and  single,  and  shares  in  proportion 16  03  3 

Doubloon,  1801 15  53  8 

Pistole,  1801 3  88  8 

Coronilla,  gold  doll.,  or  vintem,  1801 98  2 

U.  S.  AMERICA. 

Eagle,  coined  before  July  31, 1834 *. .  .10  66  8 

Eagle,  coined  after  July  31, 1834 10  . .    . 

Shares  in  proportion. 


VALUE  OF  FOREIGN  MONEY. 


CANADA,  NOVA  SCOTIA,  &c. 


A  Farthing. . 
4  Farthings  = 
12  Pence 
60  Pence 
20  Shillmgs 
30  Shillings 
40  Shillings 
50  Shillings 


a  penny 

a  shilling 

a  dollar 1 

a  pound 4 

a  moidore 6 

a  half  Joe 8 

a  Fed.  Eagle 10 


1 
20 


4.1 


T 


11 


EQUATION   OF   PAYMENTS. 


41 


NORTHERN  PARTS 

ENGLAND  &  SCOTLAND. 

LONDON,  LIVERPOOL,  BRISTOL,  EDINBURGH,  GLASGOW,  AC. 

D        C  M 

A  Farthing 4.6 

2  Farthings  =  a  half-penny 9i 

2  Half-pence       a  penny 1  Si 

4  Pence  a  groat 7  4 

6  Pence  a  half  shilling 11  1.1 

12  Pence  a  shilling 22  2.2 

54  Pence  an  Ame.  dol 1     . . 

5  Shillings  a  crown 1     11  1.1 

20  ShilliRgs  a  pound  ster 4    44  4.4 

21  Shillings  an  English  guinea. . .     4    66  6.7 

BREMEN. 

3  Grotes  ==  a  double  shilling.    .         3  2 

24  Grotes  a  mark 25  5i 

48  Grotes  a  double  mark 51  1 

72  Grotes  or  3  marks  a  rix  dollar 76  6^ 

Accounts  are  kept  in  Rix-doUars  and  Grotes. 

HANOVER, 

LUNENBURG,  ZELL,  &C. 

A  Pfenning . .     . .  2.7 

3  Pfennings      =  a  dreyer 8        .2 

8  Pfennings  a  marien 2  1.9 

12  Pfennings  a  grosh 3  2.8 

8  Groshen  a  half  guilden 26  2i 

10  Groshen  a  guilden 52  5 

24  Groshen  a  rix  dollar 78  7i 

32  Groshen  a  double  guilden . .     1      5 

34  Groshen  a  ducat 1     10 

Accounts  are  kept  in  Rix- dollars,  Groshen s,  and 
Pfennings. 


wiii-UJWaB 


•^■^^mhM^ 


42 


L 


PROP,  ware's  system  of 


ETJEOPE. 

SOUTHERN  PARTS. 

PO  RTU  GAL. 


D 


A  Rhea. 
10  Reas 
20  Reas 
5  Vintins 
4  Testoons 
24  Vintins 
10  Testoons 
48  Testoons 
64  Testoons 


=  a  half  vintin 1 

a  vintin 2 

a  testoon 12 

a  crusad  of  exchange ...  50 

a  new  crusado 60 

a  milrea 1  25 

amoidore 6  .. 

a  Johannes 8  .. 


M 

n 

5 
5 


Accounts  are  kept  in  Millreas  and  Reas. 

FRANCE    AND    NAVARRE. 

PARIS,  LYONS,  MARSEILLES,  BORDEAUX,  BAYONNE,  &C. 

Of 


A  Denier 
3  Deniers 
2  Liards 

12  Deniers 

20  Sols 

60  Sols 
6  Livres 

10  Livres 

24  Livres 


=  a  Hard... 2.3 

adardene 4.6 

a  sol 9j 

a  livi-e  toumois 18  5 

an  ecu  of  exchange. ...     55  5 

an  ecu  or  crown 1      11  1.1 

a  pistole 1      85  . . 

a  Louis  d'or 4      44  4.4 

Accounts  are  kept  in  Livres,  Sous,  and  Deniers. 

SPAIN. 

32  Reals  =  a  pistole  of  exchange. ...     3    18  5 

36  Reals         a  pistole 3    72  2 

Accounts  are  kept  in  Dollars,  Reals,  &  Maravedis. 


i 


EQUATION   OF  PAYMENTS. 


43 


SPAIN— Continued. 

GIBRALTAR,   MALAGA,   DENIA,    &C. 

Velon. 

D        C  M 

A  Maravedi '. .       1.6 

2  Maravedis  =  an  ochavo 3.2 

4  Maravedis         a  quartil 6.4 

o4  Maravedis         a  real  velon 5  3.2 

15  Reals                 a  piastre  of  ex 79  6.3 

512  Maravedis         a  pistole 77  6.3 

GO  Reals  a  pistole  of  ex. ...     3    18  5 

2043  Maravedis  a  pistole  of  ex. .. .     3    18  5 

70  Reals                 a  pistole 3    72  2 

Accounts  are  kept  in  Dollars,  Reals,  ifc  Maravedis. 

BARCELONA,   SARAGOSSA,   VALENCIA,  &C. 

A  Maravedi 3.9 

16  Maravedis  =  a  soldo 6      2i 

2  Soldos  a  rial,  old  plate 12      5 

16  Soldos  a  dollar 1 

20  Soldos  a  libra 1  25 

24  Soldos  a  ducat 1  50 

60  Soldos  a  pistole 3  60 

There  are  also  Ducats  of  21  and  22  Soldos. 

Accounts  are  kept  in  Dollars,  Reals  &  Maravedis. 

ATo^^?.— Although  60  Soldos  are  equal  to  3  dollars 
and  75  cents,  the  Spanish  Pistole  is  worth  but  3  doll- 
ars and  60  cents. 


' 
4 


44 


PROF,  ware's   system  OF 


ITALY. 

GENOA,  NOVA,  CORSICA,  BASTEA,  &C. 
A    r.  •  DOM 

A  Denari g* 

12  Denari  =  a  soldi 7,9 

4  Soldi  a  clievalet 3  1.8 

20  Soldi  a  lira 15  9.2 

30  Soldi  a  testoon 23  8^ 

5  Lires  a  croisade 79  6.3 

115  Soldis  apezzoofex 92  5.9 

6  Testoons     a  genoinc i    44  4 

20  Liers  a  pistole. 3     18  5 

Accounts  are  kept  in  Lier?,  Soldis,  and  Denaris. 

CHINA. 

PEKTN,  CANTON,   &C. 

A  Cash 14 

10  Cash     =     a  candareen l  4.8 

10  Candareens  a  mace 14  8 

10  Mace,  1  oz.  G  dwt.    6  grs.  =  a  tale.     1    48 

Accounts  are  kept  here  in  Tales,  Mace,  Candareens, 
and  Cash. 


EQUATION  OF   PAYMENTS. 


45 


PROF.  WARE'S  CHALLENGE. 


From  N.  Y.  Herald,  Oct.  30,  1870. 

$10,000  has  been  deposited  with  Greenbaum  Bros  &  Co., 
Bankers,  National  Park  Bank  Building,  by  Prof.  W  Powell 
Ware,  21  West  124th  Street,  for  the  best  Rule  for  Equation  of 
Payments.  To  be  decided  by  competent  judges  on  December 
1st,  1870* 

From  N.  Y.  Standard,  Nov.  4tli,  18  TO. 

A  Chance  for  Mathematicians.  -  The  problem  of  the 
Equation  of  Payments  is  receiving  at  present  the  attention  of 
the  best  mathemaricians,  an  announcement  having  been  re- 
cently made  by  Prof  W  Powell  Ware,  of21  West  124th  Street 
of  this  city  that  he  wouldpay$10  000  for  the  best  rule."  The 
money  has  been  deposited  for  the  purpose  with  Messrs.  Green- 
baum Bros  &Co.,  Bankers*  National  Park  Bank  Building,  to 
whom  competitors  may  send  their  rules.  On  Deoember  1st  the 
successful  competitor  will  receive  payment  for  his  rule. 

From  N.  Y.  ITorld,  Nov.  13,  1870. 

The  mathematicians  have  become  very  enthusiastic  in  their 
race  for  the  $10,000  offered  by  Prof.  Ware,  of  this  city,  for  the 
best  rule  for  the  Equation  of  Payments.  The  plans  already 
received  come  from  almost  every  seetion  of  the  country,  and 
include  eom^  very  good  and  some  very  preposterous  solutions. 
All  partie*^  interes  ed  will  meet  at  12  o'clock,  on  December  1, 
1870,  at  the  Astor  House,  at  which  time  the  successful  compet- 
itor will  receive  the  reward  for  his  labor. 

From   !V.  Y.  Times,  Nov.  15,  1870. 

Equatiox  op  Payments.— Prof.  Ware's  offer  of  $10,000 
for  the  best  rule  for  the  equation  of  payments  has  drawn  out  a 
very  excitini(  competition  between  the  mathematicians  all  over 
the  country.  The  rules  already  received  by  Prof.  Ware  and 
thoMe^*sr8.  Greenblm  Brothers,  in  whose  hands  the  money 
IS  dopo>ited,  come  from  every  section  of  the  country,  and  in- 
clude pome  marvelous  mathematical  efforts.  The  award  for  the 
best  plan  will  be  made  December  1, 1870,  at  the  Astor House,  at 
which  place  all  interested  parties  will  assemble  at  12  o'clock. 


Numerous  extracts  from  different  sections  of  the  country 
omitted  for  want  of  space. 


46 


PROF,  ware's  system   OF 


DECISION  OF  THE  JUDGES. 

[true  copy.] 

"We,  the  undersigned  committee  selected  to  decide 
upon  the  different  plans  submitted  in  the  contest  for 
the  best  rule  for  the  Equation  of  Payments,  after  ma- 
ture and  careful  examination  and  test  of  plans  offered 
by  fifty-seven  competitors  (made  conjointly  and  per- 
sonally) do  declare  this  to  be  our  positive  and  final 
decisions,  viz  : 

That  the  Rule  presented  by  Prof.  W.  Powell 
Ware,  of  New  York  City,  is  the  shortest,  simplest, 
and  best,  possessing  the  greatest  utility  and  general 
adaptation,  not  only  of  the  plans  now  bofore  us,  but 
of  any  that  has  ever  come  to  our  knowledge,  and 
which  in  our  j  udgment  is  mathematically  correct. 

We  therefore  declare  that  Prof  W.  Powell  Ware, 

of  New  York,  is  duly  entitled  to  the  award  offered. 

Signed  : 

Jos.  C.  Atwood,  with  Landers,  Frary  &  Clark,  53 
Chambers  Street. 

A.  O.  Field,  with  Jordan,  Marsh  &  Co.,  184  and  186 
Church  Street. 

John  G.  Huhn,  with  Hoover,  Calhoun  &  Co.,  362 
Broad  wa5\ 

Edward  F.  Choate,  with  E.  K  Dibble  and  Co..  53 
and  55  Worth  Street. 

B.  F.  Blake,  with  Manning,  Glover  &  Co.,  109  and 
111  Worth  Street. 

We  fully  concur  in  the  above  decision — 

H.  E.  Phelps,  book-keeper  of  H.  B.  Claflin  &  Co, 
John  P.  Gaul,  with  Tetft,  Griswold  &  Kellogg. 

443  and  445  Broadwav 
Anthon  J.  Kruger,  with  Duncan,  Sherman  &  Co., 

Banker?. 
Wm.  H.  Clark,  with  Henry  Clewes  &  Co.,  Bankers, 

32  Wall  Street. 
Matthew  Bunker,  of  Benedict,  Hall  &  Co.,  134  and 

136  Grand  Street. 


X 


EQUATION   OF  PAYMENTS. 


47 


I 


I 


Prof.  W.  POWELL  WAEE'S 

MAGIC   SQUARE 


:   t 


These  columns  (added)  make  100,  forty-two 

different  ways. 


J  3  7 

9 

6 

2 

8 

4 

1  3 

7 

9 

6 

2 

8  4  1  3  7,9 

3  9   1 

7 

2 

4 

6 

8 

3  9 

1 

7 

2 

4 

6  8  3  9  17! 

7   19 

3 

8 

6 

4 

2 

7  1 

9 

3 

8 

6 

4  2  7  19  3 

9  7  3 

1 

4 

8 

2 

6 

9  7 

3 

1 

4 

8 

2  6  9  7  3  1 

6  2  8 

4  1 

3 

7 

9 

6  2 

8 

4 

1 

3 

7  9  6  2  8  4  1 

2  4  6 

8 

3  9 

1 

2  4 

6 

8 

3 

9 

17  2  4  6  8 

8  6  4 

2 

7 

1 

9 

3 

8  6 

4 

2 

7 

1 

9  3  8  6  4  2 

4  8  2 

6 

9 

7 

3 

1 

4  8 

2 

6 

9 

7 

3  14  8  2  6 

1  3  7 

9 

6 

2 

8 

4  i  3 

7 

9 

6 

2 

8  4  1  3  7,9 

3  9  1 

7 

2 

4 

6 

8 

3  9 

1 

7 

2 

4 

6  8  3  9  17 

7  19 

3 

8 

6 

4 

2 

7  1 

9 

3 

8 

6 

4  2  7  1  9  3 

9  7  3 

1 

4 

8 

2 

6 

9   7 

3 

1 

4 

8 

2  6  9  7  3  1 

6  2  8 

4 

1 

3 

7 

9 

6  2 

8 

4 

1 

3 

7  9  6  2  8  4  1 

2  4  6 

8 

3 

9 

1 

7 

2  4 

6 

8 

3 

9 

1  7  2  4  6  8  1 

8  6  4 

2 

7 

1 

9 

3 

8  6 

4 

2 

7 

1 

9    3  8  6  4  2 

4  8  2 

6 

9 

7 

o 
O 

1 

4  8 

2 

6 

9 

7 

3  14  8  2  6 

13  7  9 

6 

2 

8 

4 

1  3 

7 

9 

6 

2 

8  4  13  7  9 

3  9  i 

7 

2 

4 

6 

8 

3  9 

1 

2 

4 

6  8  3  9  17 

7  19 

3 

8 

6 

4 

2 

7  1 

9 

3 

8 

6 

4  2  7  19  3 

9   7  3 

1 

4 

8 

2 

6 

9  7 

3 

1 

4 

8 

2  6  9  7  3  1 

1 


46 


PiiOF.  ware's  system  of 


DECISION  OF  THE  JUDGES. 

[true  copy.] 

We,  the  undersigned  committee  selected  to  decide 
upon  the  different  plans  submitted  in  the  contest  for 
the  best  rule  for  the  Equation  of  Payments,  after  ma- 
ture and  ciireful  examination  and  test  of  plans  offered 
by  fifty-seven  competitors  (made  conjointly  and  per- 
sonally) do  declare  this  to  be  our  positive  and  final 
decisions,  viz  : 

That  the  Rule  presented  by  Prof.  W.  Powell 
Ware,  of  New  York  City,  is  the  shortest,  simplest, 
and  best,  possessing  the  greatest  utility  and  general 
adaptation,  not  only  of  the  plans  now  before  us,  but 
of  any  that  has  ever  come  to  our  knowledge,  and 
which  in  our  j  udgment  is  mathematically  correct. 

We  therefoi^  declare  that  Prof  W.  Powell  Ware, 

of  New  York,  is  duly  entitled  to  the  award  offered. 

Signed  : 

Jos.  C.  Atwood,  with  Landers,  Frary  &  Clark,  58 
Chambers  Street. 

A.  O.  Field,  with  Jordan,  Marsh  &  Co.,  184  and  186 
Church  Street. 

John  G.  Huhn,  with  Hoover,  Calhoun  cfe  Co.,  362 
Broadway. 

Edward  F.  Clioate,  with  E.  R.  Dibble  and  Co.,  53 
and  55  Worth  Street. 

B.  F.  Blake,  with  Manning,  Glover  &  Co.,  109  and 
111  Worth  Street. 

We  fully  concur  in  the  above  decision — 

H.  E.  Phelps,  book-kpeper  of  H.  B.  Claflin  &  Co, 
John  P.  Gaul,  with  Teifr,  Griswold  &  KeUogg. 

44.3  and  445  Broadwav 
Anthon  J.  Kruger,  with  Duncan,  Sherman  &  Co., 

Bankers. 
Wm.  H.  Clark,  with Henrv  Clewes  &  Co., Bankers, 

32  Wall  Street. 
Matthew  Bunker,  of  Benedict,  Hall  &  Co.,  134  and 

136  Grand  Street. 


( 


EQUATION  OP  PAYMENTS. 


47 


Prof.  W.  POWELL  WAEE'S 


MAGIC    SQUAKE. 


These  columns  (added)  make  100,  forty-two 

different  ways. 


1 

3 

7 

9 

6 

2 

8 

4 

1 

3 

7 

9 

6 

2 

8 

4 

1 

3 

7 

f) 


3    7   9 


9  1 


7 


19  3 

7    3  JT 

2   8  4 

6  8 


4 
G 

8 
3 
9 
1 

7 


2 


6  2  8 

2  4  6 
8  6  4 
4  8  2 
1 

3  9 


3    7 


4  2 

2  6 

7  9 
1  7 
9  3 

3  1 

8  4 
6  8 


4   2 


4 

6 

8  2  6 

3  7  9 

9^7 

i  9  3 

7  3  1 


7  1  .9 
9  7  3 

6  2  8 

2  4  6 

8  6  4 
4  8  2 
13  7 

3  9  J 

7  i  9 

9  7  3 
6  2  8 
2  4  6 

8  6  4 

4  8  2 


4  1 

8  3 

2  7 

6  9 

9  6 

7  2 

3  8 
1  4 

4  1 

8  3 

2  7 

6  9 

9  6 

7  2 

3  8 

1  4 

4  1 

8  3 

2  7 
6  9 


7 
1 
9 
3 
8 
6 
4 


3 

9 
1 

i 

2 
4 
6 

8  2 

3  7 

9  1 
1  9 

7  3 

2  8 

4  6 

6  4 

8  2 

3  7 

9  1 
1    9 

7  3 


9  6 

7  2 

3  8 

1  4 

4  1 

8  3 

2  7 

6  9 

9  6 

7  2 

3  8 

1  4 

4  1 

8  3 

2  7 

6  9 

9  6 

7  2 

3  8 
1  4 


2  8 
4  6 
6  4 
8  2 

3  7 


9 
1 
7 
2 
4 
6 


1 
9 
3 
8 
6 
4 


4  1 

8  3 
2  7 

6  9 

9  6 

7  2 


3 
1 
4 
8 
2 


8 
4 
1 
3 

7 


8  2 

3  7 

9  1 

1  9 

7  3 

2  8 

4  6 
6  4 

8  2 


6  9 
9  6 

7  2 

3  8 

1  4 

4  1 

8  3 

2  7 
6  9 


3 
9 
1 

7 

2 

4 

6 

8 

3 

9 

1 

i 

2 

4 

6 

8 

3 

9 

1 


7  9 

1  7 
9  3 

3  1 

8  4 
6  8 

4  2 

2  6 
9 


ry 
i 

1 

9 
3 

8 


7 
3 
1 
4 

6  8 
4  2 
2  6 

7  9 
1  7 

9  3 
3i 


<    ■ 


RANKIN'S  PERPETUAL  ALMANAC, 


BOOK  FORM, 


TWO  MONTHS  TO  A  PAGE. 


-OO^^OO- 


PHILADELPHIA : 
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624,  626  &  628  MARKET  STREET. 


I 


Entered  according  to  Act  of  Congress,  in  the  year  1873,  by 

A.  N.  RANKIN, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 

ELECTROTYPED  BT  J.  FAUAN  k  SON,  PHILADELPHIA. 


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1  1777 

1  1778 

1  i77J 

1<80| 

11781 

1782 

1  1783 

1784 

1  1785  1 

1786 

11787 

1788 

1  1789 

1  1790 

1791  1 

1792 

1 

1793 

1  1794 

1  1795 

1  1796 

17H7 

1  1798 

1799 

11800 

1  1801 

1  1802 

1803  1 

1804 

1 

1805 

1  1806 

1  1807 

1  1808 

1809 

1  1810 

1811 

1  1812 

1 

1  1813 

1814  1 

1816 

11816 

1  1817 

1818 

1  1819 

18.:0  1 

1  1821 

1822 

1  1823 

1824 

1825  j 

1826 

1  1827 

18  J8 

1829 

1  1830 

1831  1 

1832 

1 

183;^ 

1834 

1  1835 

1  1^36 

1837 

1  1838 

1839 

1840  1 

1  1841  1 

1842  1 

1843 

11844 

1845  1 

1846 

1  1847  1 

1848  1 

1  1849 

1850 

1851  1 

1852 

1N53  1 

1854 

1  1865 

1856 

1857 

1  1858  1 

1859  1 

1860 

1 

1861 

1862 

1863 

1  1864  1 

1866 

1866 

1867 

1868  1 

1869  1 

1870 

1871 

1872 

1873  1 

1874 

1S75  1 

1876  1 

1877 

1878  1 

1879  1 

1880 

1 

1881  1 

1882 

1^83 

1884  1 

1885 

18-6  1 

1887  1 

1888 

1889  1 

1890  1 

1891 

1892  1 

1893 

189 

1895  1 
1901  1 

1896  1 

1897  1 

1898  1 

1899 

1900 

1902  1 

1903 

1904  1 

1905  1 

1906 

1907  1 

1908  1 

1909 

1910  1 

1911  1 

1912 

1913  1 

1914 

1915  1 

1916  1 

1 

1917 

191S  I 

1919  1 

1920  1 

1 

1921  1 

1922  1 

1923 

1924  1 

1925  1 

1926  1 

1927  1 

1928  1 

1929  1 

19:i0  1 

1931  1 

1932  1 

1933  1 

1934 

1935 

1936  1 

1937  1 

1938  1 

1939  1 

1940 

1941  1 

194'^ 

1943  1 

1944  1 

1 

1945 

1946  1 

1947  1 

1948  1 

1 

1949  1 

1950 

1951 

1952  1 

1953  1 

1954  1 

1955  1 

1956  i 

February.  | 

Mo.  1 

Tu.  1 

We. 

Th.  1 

Fr.  1 

Sat. 

8. 

1  4|11| 

18  1  2.M 

Tu.  1 

We.  1 

Th.  1 

Fr.  1 

Sat. 

S. 

1  Mo. 

1  6|12| 

19  1  26 

We.  ( 

Th.  1 

Fr. 

Sat.  1 

8.  1 

Mo. 

Tu. 

1  6|13| 

20  1  27 

Th.  1 

Fr.  1 

Sat.  1 

8.  1 

Mo.  1 

Tu.  1 

We 

1  7|14| 

21  (28 

Fr.  1 

Sat.  1 

8.  1 

Mo. 

Tu.  1 

We.  1 

Th. 

1|  8|15j 

22  1  29 

Sat.  1 

s. 

Mo.  1 

Tu.  1 

We.  I 

Th.  1 

Fr. 
Sat. 

2 1  9  1  16  1 

23  1 

8.  1 

Mo.  1 

Tu.  1 

We.  1 

Th.  1 

Fr.  I 

3  j 10  1  17  1 

24| 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  cohimn 

4  1  11 


ill 


March. 


April. 


25 


5  I  12  j  19  I  26 


6  I  13  I  20  I  27 


7  I  14  I  21  I  2S 


I  I    8  I  15  I  it  I  v9 


2  I    9  I  16  I  23  I  3() 


3  I  10  I  17  I  24  I  31 


1  I    8  I  lo  I  22  I  29 


2  1    9  I  16  I  23  I  30 


3  I  10  I  17  I  2H 


4  I  11  I  18  I  2o  I 


5  I  12  I  19  I  2r,  I 


6  I  13  I  2(»  I  27  I 


7  IIH  21  I  J8  I 


Mo.  \  Tu.    I  We.  I  Th.    |  Fr.    |  Sat. 


1811 


1839 


1867 


1895 


1907 


Tu.    I  We.  I  Th.    I  Fr.    |  Sat.  |  S- 


Sat.  I  S,  \  Mo.  i  Tu.  I  We.  |  Th. 
S.  I  Mo.  I  Tu.  I  We.  I  Th.  |  Fr. 
1771 


I  1772  I  1773  I  1774  (  1775 


1782 j  1783  I 


1788  I  17S9  I  1790  |  1791  | 


1793  I  1794  I  1795 


1799  I  1800  I  1801  I  1802  |  1803  | 


1805  I  1806  I  1807 


I  1812  I  1813  I  1814  I  1815 


1828  I  1829  I  1830  |  1831  ( 


18:^3  I  1834  I  1835 


I  1840  I  1841  I  1842  J  1843 


1844  I  1845  I  1846  |  1847  I 


1850  I  18ol  I 


1856  I  1857  I  1858  |  1859  | 


1861  I  1862  I  1863 


I  1868  I  1869  I  1870  |  1871 


1872  I  1873  I  1874  |  1875  | 


1878  I  1879  I 


1884  I  1885  I  18-6  |  1887  | 


1889  I  1890  I  1891 


1901  I  190 J  I  1903 


I  1908  I  1909  I  1910  I  1911 


I91«  I  1919  I 


1924  I  1925  I  1926  |  1927  | 


1929  I  1930  I  1931 


1935 


1936  I  1937  I  1938  |  1^39 


s. 

Mo 


We.  I  Th.    I  Fr.     |  Sat.   |  S.    I  Mo.   |  Tu. 
Th.    i  Fr.     I  Sat.   |  S.    |  Mo.  |  Tu.    jlVe. 


Fr.     I  Sat.   I  S.    I  Mo.  |  Tu.    |  We.  |  Th. 


Fi\ 
Sat. 


1776  I  1777  I  1778  |  1779  |  |  17bO  |  1781 

~  1784  I  1785  i  1786  |  1787 

1792 


I  1796  I  1797  I  1798 


1804 


I  1808  I  1809  I  1810 


1816  I  1817  I  1818  I  1819  |     |  ISiO  j  1821 
1822  I  1823  I     I  1824  {  1825  |  1826  |  1827 


1832 


I  lb36  I  1837  I  1838 


I  1848  I  1849 


1852  I  1853  I  1854  |  1855 

i860 


I  1864  I  1865  I  1866 


I  1876  I  1877 


1880  I  1881  I  1882  |  1883 


1888 


I  1892  I  1893  I  1894 


I  1896  \   1897  I  1898  I  1899  |  1900 


I  1904  I  1905  I  1906 


1912  I  1913  I  1914  \  1915  |     |  1916  |  1917 


1920  I  1921  I  1922  I  1923 

192^ 


I  1932  I  1933  j  1934 


1940  I  1941  I  1942  |  1943  |     |  1944  I  1945 


1946  I  1947  I 


1948  I  1949  I  1950  |  1951 


1952  I  1953  I  1954  |  1955  | 


1966 


Mo.  I  Tu.    \  We.   I  Th.    |  Fr.     |  Sat.  |  g. 


Tu.    I  We.  I  Th.    I  Fr.     |  Sat.  |  JS.    |  Mo. 


VVeJTh.    I  Fr.    (  Sat.  |  S.    '  Mo.   (  Tu. 


Th.    I  Fr.     I  Sat.  |  g.    |  Mo.   |  Tu.    |  We 


Fr.     I  Sat.  I  S.     I  Mo.    |  Tu.    |  We.  |  Th. 


Sat.   I  S-    I  Mo.   I  Tu.    I  We.   |  Th.     I  Fr. 


8.    I  Mo.  I  Tu.    I  W  e.  I  Th.    |  Fr.     |  Sat. 


The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 


Mo.  1  Tu.  1  We.  1  Th.  |  Fr.  |  Sat.  |  g. 

1  6  1  13  1  20  1  27 

Tu.  I  We.  1  Th.  1  Fr.  |  Sat.  |  g.  |  Mo. 

1  7  1  14  1  21  1  28 

We.  1  Th.  1  Fr.  |  Sat.  |  g.  |  Mo.  |  Tu. 

1  1  8  1  15  1  22  1  29 

Th.  I  Fr.  1  Sat.  |  g.  |  Mo.  |  Tu.  |  We. 

2  1  9  1  16  1  23  1  30 

Fr.  I  Sat.  1  g.  1  Mo.  |  Tu.  |  We.  |  Th. 

3  1  10  1  17  1  24  1  31 

Sat.  1  g.  1  Mo.  1  Tu.  1  We.  |  Th.  |  Fr. 

4  1  11  1  18  1  25  1 

g.  1  Mo.  1  Tu.  1  We.  1  Th.  |  Fr.  |  Sat. 

5  12  1  19  1  26  1 

1771  1     1  1772  1  1773  |  1774  j  1775  | 

May. 

1776  1  1777  1778  |  1779  |     j  1780  |  1781 

1782  1  1783  1     1  1784  (  1785  |  1786  |  1787 

• 

1  1788  1  1789  1  1790  |  1791  |     |  1792 

1793  1  1794  j  1795  |     |  1796  |  1797  |  1798 

1799  1  1800  1  1801  I  1802  |  1803  |     |  1804 

1805  1  1806  1  1807  |     |  1808  |  1809  |  1810 

1811  1     1  1812  1  1813  1  1814  |  1816  | 

1816  1  1817  1  1818  1  1819  |     |  1820  (  1821 

1822  1  1823  1     j  1824  |  1825  j  1826  |  1827 

1  1828  1  1829  J  1830  |  1831  |     |  1832 

1833  1  1834  1  1835  1     |  1836  |  1837  |  1838 

1839  I     I  1840  1  1841  |  1842  |  1843  | 

1844  1  1845  j  1846  |  1847  |     |  1848  |  1849 

1850  1  1851  1     1  1852  |  1863  |  1854  |  1855 

1  1856  1  1857  1  1858  |  1859  |     |  1860 

1861  I  1862  I  1863  |     |  1864  |  1866  |  1866 

1867  I     I  1868  1  1869  j  1870  1871  | 

1872  1  1873  1  1874  |  1875  |     |  1876  |  1877 

1878  1  1879  1     1  1880  |  1881  |  1882  |  1883 

1  1884  1  1885  1  18^6  |  1887  |     |  1888 

1889  1  1890  1  1891  |     |  1892  |  1893  |  1894 

1895  1     1  1896  1  1897  |  1898  |  1899  1900 

1901  1  1902  1  1903  1     1  1904  1  1905  |  1906 

1907  J     I  1908  1  1909  |  1910  |  1911  | 

1912  1  1913  1  1914  1  1915  |     |  1916  |  1917 

1918  1  1919  1     1  1920  1  1921  |  1922  |  1923 

1  1924  1  1925  1926  |  1927  [     |  1928 

1929  1  1930  1  1931  (     |  1932  |  1933  |  1934 

1935  1     1  1936  j  1937  |  1938  1939  | 

1940  1  1941  1  1942  |  1943  |      1944  |  1945 

1946  1  1947  1     1  1948  1949  |  1950  |  1951 

1  1952  1  1953  1  1954  |  1956  |      1966 

June. 

Mo.  1  Tu.  1  We.  1  Th.  |  Fr.  |  Sat.  |  g. 

1  3  1  10  !  17  1  24 

Tu.  1  We.  1  Th.  1  Fr.  |  Sat.   g.  |  Mo. 

1  4|11  |18|26 

We.  1  Th.  1  Fr.  |  Sat.  |  g.  |  Mo.  Tu. 

1  6  1  12  1  19  1  26 

Th.  1  Fr.  1  Sat.  |  g.  |  Mo.  |  Tu.  |  We. 

1  6  1  13  1  20  1  27 

Fr.  1  Sat.  1  g.  1  Mo.  I  Tu.  |  We.  |  Th. 

1  7  1  14  1  21  1  28 

Sat.  1  g.  1  Mo.  1  Tu.   We.  |  Th.  I  Fr. 

1  1  8  1  15  1  22  1  29 

g.  1  Mo.  1  Tu.  1  We.  1  Th.  |  Fr.  |  Sat. 

2  1  9  1  16  1  23  1  30 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 

1  1  8  1  15  1  22  1  29 

Mo.  j  Tu.  1  We.  1  Th.  |  Fr.  |  Sat.  |  S. 

2  1  9  1  16  1  23  1  30 

Tu.  1  We.  1  Th.  1  Fr.  |  Sat.  |  g.  |  Mo. 

3  1  10  1  17  1  24  1  31 

We.  1  Th.  1  Fr.  |  Sat.  |  S.  1  Mo.  |  Tu. 

4  1  11  1  18  1  2.)  1 

Th.  1  Fr.  1  Sat.  |  g.  |  Mo.  |  Tu.  |  We. 

5  1  12  j  19  I  26  1 

Fr.  1  Sat.  1  S.  1  Mo.  |  Tu.  |  We.  |  Th. 

6  1  13  1  20  1  27  1 

|Sat.  1  S.   Mo.  1  Tu.  1  We.  |  Th.  |  Fr. 

7  1  14  1  21  1  28  1 

S.   Mo.  1  Tu.  1  We.  1  Th.  |  Fr.  |  Sat. 

July. 

1771      1  1772  1  1773  |  1774  |  1775  | 

1776  1  1777  1  1778  |  1779  |     j  1780  |  1781 

1782  1  1783  1     1  1784  |  1785  |  1786  |  1787 

1  1788  1  1789  1  1790  |  1791  |     |  1792 

1793  1  1794  1  1795  j     |  1796  |  1797  |  1798 

1799  1  1800  1  1801  1  1802  |  1803  |     j  1804 

1805  1  1806  1  1807  |     |  1808  |  1809  |  1810 

1811  1     1  1812  1  1813  1  1814  |  1815  | 

1816  1  1817  1  1818  1  1819  |     |  1820  |  1821 

1822  1  1823  1     1  1824  |  1825  |  1826  |  1827 

1  1828  1  1829  1  1830  1831  |     |  1832 

1833  1  18;U  1  1835  |     |  1836  |  1837  |  1838 

1839  1     1  1840  1  1841  |  1842  |  1843  | 

1844  1  1845  1  1846  |  1847  |     |  1848  |  1849 

1850  1  1851  1     1  1852  |  1853  |  1854  |  1855 

1  1856  1  1857  1  1858  |  1859  |     |  1860 

1861  I  1862  1  1863  |     |  1864  |  1865  |  1866 

1867  1     1  1868  1  1869  |  1870  |  1871  | 

1872  1  1873  1  1874  |  1875  |     |  1876  1877 

1878  1  1879  1     1  1880  (  1881  |  1882  |  1883 

1  188H  1885  1  18^6  |  1887  |     |  1888 

1889  1890  1  1891  |     |  1892  |  1893  |  1894 

1895  1     1  1896  1  1897  |  1898  |  1899  (  1900 

1901  1  1902  1  1903  1     1  1904  1  1905  |  1906 

1907  1     1  1908  1  1909  |  1910  |  1911  | 

1912  1  1913  1  1914  1  1915  |     |  1916  |  1917 

1918  1  1919  1     1  1920  1  1921  |  1922  |  1923 

1  1924  1  1925  1  1926  [  1927  |     |  1928 

1929  1  19;i0  1  1931  1     1  1932  1  1933  (  1934 

1935  1     1  1936  1  1937  |  1938  f 1939  | 

1940  1  1941  1  1942  |  1943  |     |  1944  |  1945 

1946  1  1947  1     1  1948  |  1949  \  1950  |  1951 

August. 

1  1952  1  195:3  1  1954  1  1955  1     |  1956 

1  5  1  12  1  19  1  26 

Mo.  1  Tu.  1  We.  1  Th.  (  Fr.  |  Sat.  |  g. 

1  6  1  13  1  20  1  27 

Tu.  1  We  1  Th.  1  Fr.  |  Sat.  |  S.  1  M« 

1  7  1  14  1  21  1  28 

We.  !  Th.  1  Fr.   Sat.  |  S.  1  Mo.  j  Tu 

1  1  8  1  15  1  22  1  '29 

Th.  1  Fr.  1  Sat.  |  g.   Mo.  |  Tu.  |  W  e 

2  1  9  1  10  23  1  30 

Fr.  1  Sat.  1  S.  (  Mo.  |  Tu.  (  We.  f  Th. 

3|10|17|2t  31 

Sat.  1  S.  1  Mo.   Tu  1  We.  |  Tli.  1  Fr. 

4  1  11  !  18  1  25  1 

S.  1  Mo.  1  Tu.  1  We.  Th  |  Fr.  |  Sat. 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column 

• 

Mo.  iTu.  I  We.  |Th.  |  Fr.  |  Sat.  |  g. 

Tu^j  We.  I  Th.  I  Fr.  |  Sat.  |  g,  |  M^ 

We.  I  Th.  I  Fr.  |  Sat.  |  g.  |  Mo.  I  Tu. 

Th.  ~ 


Fr. 


I  Fr.  j  Sat.  I  g,  I  Mo.  |  Tu.  |  We. 
T«at.  I  g.  I  Mo.  I  Tu.  I  We.  |  Th. 


Sat.  I  g,  I  Mo.  I  Tu.  I  We.  |  Th.  |  Fr. 


g. 


1771  ( 


I  Mo.  I  Tu.  I  We.  I  Th^|Fr~fs^- 
I  1772  I  1773  I  mTjlTTSl 


1776  I  1777  j  1778  I  J779j__|T7^  |  i7«i 
1782^1  1783  I     [17841  1785  |  1786  j  1787 
I  1788  I  1789  I  1790  |  1791  |     \vm 


1793  I  1V94  I  1795  |     |  1796  |  1797  I  1798 


1799  I  1800  J  1801  I  1802  |  1803  | fl804 

1805  I  1806  I  1807  |     |  1808  |  1809  i  1810 
1811  I     i  1812  I  1813  I  1814TT8151 


1816  I  1817  I  1818  I  1819  | 

1822  I  1823  I     [  1824  |  1825  |  1826  |  1827 


I  1820  I  1821 


I  1828  I  1829  I  1830  |  1831  |  ~   (1832 


183;^  I  1834  I  1835  |     |  1836  |  1837  I  1838 


1839  I 


1840  I  1841  I  1842  |  1843  | 


1844  I  1845  j  1846  |  1847  |     |  1848  I  1849 


1850  I  1851  i     I  1852  j  1853  |  1854  |  1855 


I  1856  (  1857  I  1858  |  1859  | 

1864 


1861  I  1862  I  1863  | 
1867  I 


I  1860 


1865  I  1866 


I  1H68  I  1869  I  1870  |  1871  | 


1872  I  1873  I  1874  |  1875  |     |  1876  |  1877 
^878  I  1879  I     I  1880  |  1881  |  1882  I  1883 


1889 


I  1884  I  1885  I  18>'6  |  1887  | 
1890  I  1891  I 


I  1888 


I  1892  I  1893  I  1894 


1895  I     I  1896  I  1897  |  1898  |  1899  |  1900 
1901  I  1902  I  19031     I  1904  |  1905  |  1906 


1907  I  I  1908  I  1909  |  1910  |  1911  | 
1912  I  1913  I  1914  I  1915  |  |  1916  j  1917 
1918  I  1919  I  j  1920  I  1921  |  1922  |  1923 
I  1924  I  1925  I  1926  \  1927  |     fl928 


1929  I  1930  I  1931  |     |  1932  |  1933  |  1934 


1935  I 


1936  I  1937  I  1938  |  1939  | 


1940  I  1941  I  1942  |  1943  |  |  1944  |  1945 


1946  I  1947  I  I  1948  |  1949  |  1950  |  1951 


i  1952  I  1953  I  1954  |  1955  |  |  1956 


Mo.  I  Tu.    \  We.    I  Th.    |  Fr.    |  Sat.  |  g. 


Tu.    I  We    I  Th.    I  Fr.     |  Sat.   |  g.    )  Mo. 


We.  (  Th.    I  Fr.     |  Sat.   |  g.    |  Mo.   |  Tu. 
'Hi.    I  Fr.     I  Sat.  |  g.    |  Mo.  i  Tu.    I  We 


Fr.    i  Sat.  I  g.    I  Mo.   |  Tu.    (  We.  |  Th. 


Sat.   I  g.    I  Mo.   I  Tu.    I  We.  |  Th.    |  Fr. 
"g.    I  Mo.  I  Tu.    I  We.  I  Th.    |  Fr.     |  Sat. 


i  2  I    9  1 16  I  23  I  30 


3  1 10  1 17  I  24 1 


i  4  1 11  1 18  I  25  I 


6  I  12  I  19  j  26  I 


6  1 13  I  20  I  27  I 


I  7  1 14  I  21  I  28  I 


1 1  8  1 15  I  22  I  29 


September. 


October. 


I    7  I  14  I  21  I  28 


1  I    8  I  15  I  22  I  29 


2  I    9  I  16  I  23  I  30 


3  I  10  I  17  I  24  I  31 


4  I  11  I  18  I  25  I 


5  I  12  I  19  I  26  I 


6  I  13  I  20  I  27  I 


The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 


-  '  .Mil  ■ 


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1 


COLUMBIA  UNIVERSITY  LIBRARIES 

This  book  is  due  on  the  date  indicated  below,  or  at  the 
expiration  of  a  definite  period  after  the  date  of  borrowing,  as 
provided  by  the  rules  of  the  T-iibrary  or  by  special  arrange- 
ment with  the  Liibrarian  in  charge. 

DATE  BORROWED 

DATE  DUE 

DATE  BORROWED 

1 
DATE  DUE 

C28(i141)m100 

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( 


D486 


Ware,  W.  Powell 


W22 


Prof.  Ware's  $10,000  prize  rule 
for  the  equation  of  payments. 


rP<^<^ 


U/yy 


Al9l  0\\oV\ 


WAY  nt|1994 


I 


COLUMBIA  UNIVERSITY  LIBRARIES 


004141 


7240 


i 


SEP  28  19** 


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